Cremona's table of elliptic curves

12950 = 2 · 5² · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 37+	Signs for the Atkin-Lehner involutions
Class	12950s	Isogeny class
Conductor	12950	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	8400	Modular degree for the optimal curve
Δ	-202343750 = -1 · 2 · 58 · 7 · 37	Discriminant
Eigenvalues	2- -3 5- 7-  4 -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-180,1197]	[a1,a2,a3,a4,a6]
j	-1642545/518	j-invariant
L	1.6870125370557	L(r)(E,1)/r!
Ω	1.6870125370557	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	103600bx1 116550cp1 12950a1 90650dd1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12950s1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-3	-	-	4	-2	-6	-2	0	2	-3	+	6	7	-12	0	0	2	4	8	8	-8	7	-1	-2

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Quadratic twists for elliptic curve 12950s1

-4	-3	5	-7
103600bx1	116550cp1	12950a1	90650dd1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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